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On holomorphic extensions from spheres in ℂ2

Published online by Cambridge University Press:  14 November 2011

Josip Globevnik
Josip Globevnik
Affiliation:
Institute of Mathematics, Physics and Mechanics, E.K. University of Ljubljana, Ljubljana, Yugoslavia
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Synopsis

A theorem of Rudin states that if B is the open unit ball in ℂN, N > 1, if 0<ρ < 1, if is the family of all complex lines in ℂN at a distance ρ from the origin and if f ∈ C(∂B) is such that for every Λ∈ the function f|Λ∂B has a continuous extension to Λ ∩ B which is holomorphic in Λ ∩ B, then f has a continuous extension to B which is holomorphic in B. In this paper we show that when N = 2, the theorem still holds if is replaced by a considerably smaller family.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 113 - 120
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

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